Finite Group Databasebeta

← #13254757

Subgroups — #13254757

Order 1792.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739893C212yesmaximal
2#11736482C211yesmaximal, characteristic
3C7×#1985C211yesmaximal, characteristic
4#11727555C212yesmaximal
5#11725514C211yesmaximal, characteristic
6C2×C4×C7×Q8C2211yescharacteristic
7#90161C2212yes—
8C2×C7×C4⋊C8C2211yescharacteristic
9C2×C7×#97C2211yescharacteristic
10#90000—22no—
11#89888—22no—
12#89803—22no—
13#89802—24no—
14#89792—22no—
15#89743—22no—
16#89698C2212yes—
17#89622—22no—
18#89621—22no—
19C7×#336—22no—
20#89260—24no—
21#10031—71nomaximal, Sylow
22C22×C7×Q8D411yescharacteristic
23C22×C7×C8—21no—
24C22×C7×C8D412yes—
25C4×C7×Q8—22no—
26C4×C7×Q8—22no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C42×C7—21no—
30C2×C42×C7C2311yescharacteristic
31C2×#1144—24no—
32#6489—22no—
33#6487—22no—
34#6487—22no—
35C2×Dic28—22no—
36#6433—22no—
37#6432D412yes—
38#6432D412yes—
39C4×Dic14—22no—
40C4×Dic14—22no—
41C7×C4⋊C8—22no—
42C7×#97—22no—
43#6409—24no—
44C22⋊(C7⋊C8)—22no—
45#6392—22no—
46#6390—24no—
47#6384—24no—
48#6382—24no—
49C4⋊(C7⋊C8)—22no—
50#6377D414yes—
51#3249—71no—
52#3113—72no—
53#1985D711yescharacteristic
54#1531—72no—
55#1290—71no—
56C2×C7×Q8—22no—
57C2×C7×Q8—42no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7C2×D411yescharacteristic
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7#4111yescharacteristic
63C2×Dic14—22no—
64C2×Dic14—22no—
65C2×C7×C8—22no—
66C2×C7×C8—22no—
67C2×C7×C8—41no—
68C2×C7×C8—41no—
69C2×C7×C8—42no—
70C7×C4⋊C4—22no—
71C7×C4⋊C4—42no—
72C42×C7—41no—
73C42×C7—41no—
74C42×C7C2×D412yes—
75C42×C7C2×D412yes—
76C22⋊Dic7—42no—
77#1144—48no—
78C4⋊Dic7—22no—
79C4⋊Dic7—22no—
80C4⋊Dic7—22no—
81C4⋊Dic7—22no—
82Dic7⋊C4—42no—
83Dic7⋊C4—42no—
84C4×Dic7—42no—
85C2×C7⋊C8—24no—
86Dic28—82no—
87#533—72no—
88C2×C4×Q8C2×D711yescharacteristic
89#483—142no—
90#477—142no—
91#475—142no—
92#467—142no—
93#462—142no—
94#462—142no—
95#451—142no—
96#441—144no—
97#432—72no—
98C2×C4⋊C8C2×D711yescharacteristic
99C2×#97C2×D711yescharacteristic
100#336—22no—
101#330—144no—
102C23×C7#12111yescharacteristic
103C7×Q8—24no—
104C7×Q8—42no—
105C2×C4×C7—22no—
106C2×C4×C7—21no—
107C2×C4×C7—21no—
108C2×C4×C7—22no—
109C2×C4×C7—41no—
110C2×C4×C7—41no—
111C2×C4×C7—41no—
112C2×C4×C7—41no—
113C2×C4×C7—42no—
114C2×C4×C7#12012yes—
115C2×C4×C7#12011yescharacteristic
116C2×C4×C7#12112yes—
117C2×C4×C7#12711yescharacteristic
118C2×Dic7—42no—
119C2×Dic7—42no—
120Dic14—44no—
121Dic14—42no—
122Dic14—42no—
123C7×C8—42no—
124C7×C8—42no—
125C7⋊C8—44no—
126C22×Q8D2811yescharacteristic
127C2×Q16—142no—
128C2×Q16—144no—
129C22×C8—21no—
130C22×C8C22⋊D712yes—
131C4⋊Q8—72no—
132C4⋊Q8—72no—
133#125—142no—
134C22⋊Q8—142no—
135C22⋊Q8—142no—
136C4×Q8—22no—
137C4×Q8—22no—
138C4×Q8—142no—
139C4×Q8—142no—
140#117—142no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4D2811yescharacteristic
143C2×C42—21no—
144C2×C42C22×D711yescharacteristic
145#107—142no—
146#106—144no—
147C4⋊C8—22no—
148C4⋊C8—142no—
149#103—144no—
150#103—144no—
151#103—144no—
152C22⋊C8—142no—
153#97—22no—
154#97—74no—
155C22×C7—21no—
156C22×C7—21no—
157C22×C7#39211yescharacteristic
158C22×C7#47312yes—
159C4×C7—21no—
160C4×C7—22no—
161C4×C7—22no—
162C4×C7—42no—
163C4×C7—81no—
164C4×C7#45511yescharacteristic
165C4×C7#45611yescharacteristic
166Dic7—82no—
167Dic7—82no—
168C2×Q8—22no—
169C2×Q8—42no—
170C2×Q8—142no—
171C2×Q8—142no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4C2×D2811yescharacteristic
175C22×C4#115711yescharacteristic
176C22×C4C2×C22⋊D711yescharacteristic
177Q16—288no—
178Q16—562no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—42no—
184C2×C8—144no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—142no—
188C4⋊C4—142no—
189C4⋊C4—142no—
190C4⋊C4—142no—
191C4⋊C4—282no—
192C4⋊C4—282no—
193C22⋊C4—282no—
194C42—41no—
195C42—41no—
196C42—282no—
197C42D4×D712yes—
198C42D4×D712yes—
199C2×C7—22no—
200C2×C7#200711yescharacteristic
201C2×C7#201011yescharacteristic
202C2×C7#202011yescharacteristic
203C23#649311yescharacteristic
204Q8—24no—
205Q8—42no—
206Q8—284no—
207Q8—282no—
208Q8—282no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—282no—
219C2×C4—282no—
220C2×C4#644512yes—
221C2×C4#644712yes—
222C2×C4#650011yescharacteristic
223C2×C4#650311yescharacteristic
224C8—42no—
225C8—42no—
226C8—284no—
227C7#1003111yescharacteristic, complemented, Sylow
228C22—21no—
229C22—21no—
230C22#8973211yescharacteristic
231C22#8991512yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—562no—
238C4—562no—
239C4#8983311yescharacteristic
240C4#8986711yescharacteristic
241C2—22no—
242C2#1172744811yescharacteristic
243C2#1172774711yescharacteristic
244C2#1172776211yescharacteristic
subgroupG/H
centerC22#89732
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1985C2
socleC22×C7#392
prime radicalC23×C7#121
hypercenter#1985D7
hypocenterC7#10031
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
227. C7#10031semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117398932
#117364822
C7×#19852
#117275552
#117255142
#100317